41. Marian Gidea Homepage Subsequently, a number of mathematicians discovered unusually complex behaviorin simple equations Gaston Julia and pierre fatou in 1918, George Birkhoff http://www.neiu.edu/~mgidea/

"You cannot teach a man anything, you can only help him to find it for himself." - Galileo Galilei Curriculum Vitae Publication List Courses Seminars ... Mathematical Physics Preprint Archive INTRODUCTION I am an Associate Professor at the Department of Mathematics of Northeastern Illinois University , and a Visiting Faculty at Northwestern University I received my M.S. in Mathematics from University of Bucharest in 1992, and my Ph.D. in Mathematics from State University of New York at Buffalo in 1997. RESEARCH INTERESTS My field of research is Dynamical Systems - with a focus on Topological Methods in Dynamics, Chaos Theory, and Celestial Mechanics. The origins of Dynamical Systems are closely related to Henri Poincaré work on the three-body problem. Poicaré pointed out that " it may happen that small differences in the initial conditions produce very great ones in the final phenomena ", which can be regarded as one of the first descriptions of chaos. Subsequently, a number of mathematicians discovered unusually complex behavior in simple equations: Gaston Julia and Pierre Fatou in 1918, George Birkhoff in the 1920s, Stephen Smale in late 1950s, and Edward Lorenz in the 1960s. The prototypical example of a chaotic dynamics is the Smale horseshoe, shown right.

42. The Sahara; ; Pierre Loti and riotous town affairs to his passionate desert romance with fatouGaye . pierre Loti, perhaps the world’s most prolific, romantic and exotic http://www.columbia.edu/cu/cup/catalog/data/071030/0710308175.HTM

Order Info F.A.Q. Help Advanced ... BUY ONLINE January, 2003 cloth 200 pages ISBN: Kegan Paul New Book Bulletins The Sahara Pierre Loti Loti’s sensitive, almost sensuous, and exotic art is peculiarly fitted for such a subject as "the great sea without water," and the Spahi on the Senegal, of romantic passion and seductive smile, "undisciplined but not dissolute," whose love adventures range from sordid and riotous town affairs to his passionate desert romance with Fatou-Gaye. About the Author Pierre Loti, perhaps the world’s most prolific, romantic and exotic travel writer and novelist, was born as Julien Marie Viaud in Rochefort in Western France in 1850. A childhood fascination with exotic lands across the seas led him to embark on a naval career that enabled him to seek love and adventure in many latitudes. He drew on these real life experiences when writing the romantic novels and travel books that made him one of the most popular authors of his day. Although his prolific output brought him both fame and fortune he remained a romantic escapist and never gave up his beloved naval career. He retired from the French navy in 1910 and died in 1923. From the series Pierre Loti Library For more information, please contact

43. Julia Sets Mandelbrot called disconnected Julia sets a dust of points (Mandelbrot 79),or fatou dust (after pierre fatou 18781929) (Mandelbrot 182). http://www.mcgoodwin.net/julia/juliajewels.html

Julia Sets Site Map Julia Jewels: An Exploration of Julia Sets by Michael McGoodwin (March 2000) The infinite! No other question has ever moved so profoundly the spirit of man. David Hilbert (1862-1943) Julia set formed by f(z) = z + c where c = 0.687 + 0.312i (click on any thumbnail image to view full size) Introduction This presentation was prepared as the final assignment for the course Math 497 at the University of Washington, taught by James R. King, Ph.D. This course dealt with selected topics in the behavior of complex numbers and functions. I was prompted to take this course (noncredit) by my long-standing though latent interest in the well-known fractal objects that are defined in complex planes, the Julia and Mandelbrot Sets, and am grateful to Professor King for offering it as an extension course. Along with the Feigenbaum (logistic) bifurcation diagram and the Hénon Lorenz , and Rössler attractors, these fractal sets have come to epitomize the world of strange (i.e., fractal) attractors, and have captured the fancy and imagination of mathematicians and lay persons alike. It was my preference to attempt to survey the properties of Julia sets as broadly as possible rather than to focus solely on one or two subtopics (as might be more appropriate for the actual assignment), and this broad approach inevitably must result in some degree of superficiality. However, I have tried to avoid presenting a mere album of pretty images, and have tried to keep the discussion mainly at the mathematical level. Since the underlying mathematics is often abstruse and beyond my expertise, I have found it necessary to report some of the known properties of Julia sets without offering proof or further details.

44. Fractals returned to earlier research questions first posed between 1915 and 1930 byFrench mathematicians Gaston Julia and pierre fatou Does the iteration of http://curvebank.calstatela.edu/fractal/fractal.htm

Back to . . . Curve Bank Home The Mandelbrot Set weds the graphing of complex numbers to the recursive power of modern computers. MandelZoom takes approximately 15 seconds to load. Be patient. MandelZoom (C) Louis P. Santillan 2001-2002 Instructions: Click to zoom IN. O to zoom OUT. R to reset to the original screen. C to CHANGE COLORS. For source code, email Louis here. Back to . . . Curve Bank Home The points of a Mandelbrot Set are bounded as follows: x: -2 x y i i x i Size: radius or distance from (0,0) The full Mandelbrot Set is plotted within the inscribed circle of radius . Other views showing the fractal edge are displayed by zooming in on only a portion of the bounded area. Sample calculation: Mathematicians in the early 20th century investigated curves that had highly intricate and detailed shapes. Moreover, they realized that while a region might be bounded and thus the area finite, the perimeter or border might seem to be infinite. These curves - the Koch Snowflake for example - with finite area and infinite perimeter, were given the name of "pathological." This particular area of research in mathematics has generated colorful names: Cantor's dust, Polya's sweeps, Peano's dragons, Sierpinski's carpet and others. When the edge of a curve under many iterations is broken, repeated, scaled down, and then scaled down again as the iterations progress, the curve has now become known as a fractal. This relatively new word in mathematics was first coined by Benoit B. Mandelbrot and introduced to mathematicians and computer scientists in

45. History Of Fractals Until Benoit Mandelbrot, Gaston Julia and pierre fatou discovered selfsimilarstructures in iterative mappings in the complex plane C, such structures had http://www.math.ku.edu/~dmcneill/paper/node1.html

Next: ``Applications'' of Fractals Up: Fractals: History and Explanation Previous: Fractals: History and Explanation History of Fractals Fractals, in the most general definition, are simply self-similar structures. In this sense fractals are all around us in the shapes of a coastline, a fern, a tree, or a mountain range. A tree, for instance, is a trunk with branches and leaves, while a branch has twigs and leaves. Hence the smaller parts of a tree appear to have the same structure as the whole. Until Benoit Mandelbrot, Gaston Julia and Pierre Fatou discovered self-similar structures in iterative mappings in the complex plane C, such structures had gone largely unnoticed. Beginning in the late 1910's and into the 1920's, Julia and Fatou led the study of these self-similar structures. At that time there were no computers to produce the images we see today. Consequently interest in fractals was restricted to those very few individuals who could in some sense understand the mathematics behind the pictures that are drawn today. Julia and Fatou discovered self-similar structures born of iterative (or recursive) functions from C to C, in which each function value after the first is defined in terms of its predecessors. The functions took the form:

46. Fractals! These were invented during the first World War by Gaston Julia and pierre fatou.Julia sets can vary quite greatly in visual appearance some appear as http://www.bath.ac.uk/~ma0etd/fractals/mandlebrot.htm

The Mandlebrot Set. So who is this Mandlebrot guy anyway? And what is his set? Well, many people like to say that the Mandlebrot set is the most complex image in Mathematics. As you may have already guessed, the Mandlebrot set is a fractal. The story of how it was discovered is particularly interesting. It was one of the first fractal shapes to be discovered with the aid of computers. Mathematicians before the twentieth century had many problems when it came to difficult calculations, in particular iterative processes. This was because of the absense of computers. Computers have since allowed Mathematicians to carry out much more complicated tasks in less time and with greater accuracy. Computers are exactly what is needed to produce fractals in high resolution. The whole of the Mandlebrot set. Click to enlarge... WIthout computers images such as these would be incredibly tedious to create because of the multitude of calculations necessary for each point. When the first black and white images emerged at IBM and Harvard, even Mandlebrot could not fully understand how unique and extraordinary the pictures he and his team of programmers generated really were. With the development of technology we can now get crisper images of the set at higher magnifications. If you would like to see more pictures from the Mandlebrot set then feel free to visit the

47. DIAL - Présentation - Les Chercheurs des guerres civiles, Economie publique, Biens publics mondiaux. CLING Jeanpierre.Directeur du GIE DIAL fatou Binetou. Allocataire de recherche IRD http://www.dial.prd.fr/dial_presentation/dial_equipe_chercheurs.htm

L'équipe de DIAL CHAUVET Lisa Chargée de recherche IRD CVFrançais CVEnglish E-mail Axes de recherche Financement du développement, Aide internationale et investissements directs étrangers, Analyses empiriques de la croissance, Economie politique des guerres civiles, Economie publique, Biens publics mondiaux. CLING Jean-Pierre Directeur du GIE CVFrançais CVEnglish E-mail Axes de recherche Liens entre commerce et développement, Gouvernance Internationale. COGNEAU Denis Chargé de recherche IRD Enseignant à l’ENSAE et à l’EHESS DEA Analyse et Politiques Economiques CVFrançais CVEnglish E-mail Axes de recherche Politiques économiques dans les pays en développement, Economie de la croissance et de la répartition, Marché du travail, Pauvreté et inégalités, Mobilité économique et sociale. GUBERT Flore Chargée de recherche IRD CVFrançais CVEnglish E-mail Axes de recherche Développement rural, Economie agricole, Gestion des risques, Migration.

48. Fractals And Fractal Architecture - Characteristics 01Gaston Julia like his rival pierre fatou analyzed the phenomenon of feedback.They realized the influence of the constant “C” but they did not have the http://www.iemar.tuwien.ac.at/modul23/Fractals/subpages/223characteristics.html

Fractals and Fractal Architecture by Wolfgang E. Lorenz department of computer aided planning and architecture vienna university of technology back to: 2.2 Characteristics 2.2.1 A Fractal is Rugged 2.2.2 A Fractal is Self-Similar 2.2.3 A Fractal is Infinitely Complex ... 2.2.6 A Fractal is Common in Nature 2.2.3 Characteristics - A Fractal is Infinitely Complex Fractals are highly complex, that means zooming in will bring up more and more details of the object, a characteristic that continues until infinity. Chaotic fractals: Already in the 20ies of the 20th century the French mathematicians Gaston Julia and Pierre Fatou concerned themselves with the question of fractal geometry. Both examined what would happen to a point “Z” of the complex number-plane if the transformation was repeatedly applied to it . Gaston Julia discovered that calculating the function repeatedly might deliver unforeseen “chaotically” results. It was only in the 70ies that Mandelbrot could show the results of the formula as a picture, which needed the high capacity of computers. The Mandelbrot set is similar from scale to scale, which means zooming closer to the details there will always come up new parts looking similar to each other and sometimes to the whole - see picture 07 . The only limits are limits of capacity and, resulting from this, rounding mistakes by the computer, but also limits of the visual medium.

49. Fractals,reflections And Distortions They are called Julia sets, after the French mathematician Gaston Julia who,together with his contemporary pierre fatou, first studied them in 1918. http://www.fortunecity.com/emachines/e11/86/reflect.html

web hosting domain names photo sharing Fractals, reflections and distortions Fractals obtained from repeated reflections in circular mirrors produce breathtaking kaleidoscopic images. Understanding these pictures may give us new insights into the geometry of chaos Caroline Series Most people have become familiar in recent years with pictures of fractals - those elusive shapes that, no matter how you magnify them, still look infinitely crinkled. The pictures you saw were probably drawn by computer, but examples abound in nature - the edge of a leaf, the outline of a tree, or the course of a river. Fractal curves differ from those studied in normal geometry. The curve of a circle, for instance, if magnified sufficiently, just about - becomes a straight line. A fractal curve, on the other hand, when viewed on many different scales, from macroscopic to microscopic, reveals the same intricate pattern of convolutions. How do you construct a fractal curve? A simple example is the famous Koch snowflake, invented by Helge von Koch in 1904. It is an example of a "nowhere smooth" curve. To draw the snowflake, start with the triangle shown in Figure la. Then replace each of the sides of this triangle by a bent line as shown in Figure 1b. At the next stage, Figure 1c, each of these sides in turn is replaced by the same pattern but on a smaller scale, and so on, ad infinitum, to obtain finally the snowflake shown in Figure 1d.

50. MathFiction: Fatous Staub (Christian Mähr) This surrealistic science fiction novel about parallel worlds, computers, andthe mathematics of pierre fatou (who laid the foundations for the theory of http://math.cofc.edu/faculty/kasman/MATHFICT/mfview.php?callnumber=mf463

51. [ Wu :: Fractals | Mandelbrot ] Mathematician pierre fatou (18781929) showed that every attracting cycle for apolynomial or rational function attracts at least one critical point. http://www.ocf.berkeley.edu/~wwu/fractals/mandelbrot.html

Fractals: The Mandelbrot Set Fractal Intro Mandelbrot Sierpinski Gallery ... Return to Homepage Construction: The Mandelbrot set is the set of all complex numbers c such that iterating z <= z^2 + c does not ascend to infinity, starting with z=0. The terms z and c are complex numbers (see Note 1 for an overview of complex numbers, if necessary). "Ascend to infinity" means that z will continue to grow with each iteration; in calculus terms, it means that z diverges; more on this, as well as the initial condition z=0 , later. I will proceed with explaining simply how to graph the set, and place explanations for the mathematical intricacies in footnotes for those curious. We could probably find a few elements in the Mandelbrot set by pencil and paper, but in order to crank out enough iterations to produce even a semi-decent graph before dying of either old age or a mental segmentation fault, we will want to determine the elements of the Mandelbrot set using a simple computer program. I will use Java-like pseudocode. Let us first declare a complex number class complexNumber // A class for complex numbers.

52. Fatou A Mandelbrot set plotter for the TI82. Runs in about 1 hour If U\^2\+V\^2\ 4 , means that for this c value z will go to infinity, this wasproved by pierre fatou, 1905. * Pt-Off(X,Y) , the points not belonging to http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Fatou.html

Pierre Joseph Louis Fatou Born: 28 Feb 1878 in Lorient, France Died: 10 Aug 1929 in Pornichet, France Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Pierre Fatou Having been appointed to the astronomy post, Fatou continued to work on mathematics for his thesis. He submitted his thesis in 1906 which was on integration theory and complex function theory. Fatou proved that if a function is Lebesgue integrable, then radial limits for the corresponding Poisson integral exist almost everywhere. This result led to generalisations by Privalov Plessner and Marcel Riesz . Although not giving a complete solution, Fatou's work also made a major contribution to finding a solution to the related question of whether conformal mapping of Jordan regions onto the open disc can be extended continuously to the boundary. In 1907 Fatou received his doctorate for this important work. The book [2] presents a beautiful historical account of the global theory of iteration of complex analytic functions. Fatou enters this history in a rather complicated way and the book does an excellent job in explaining an interesting episode in the history of mathematics. In 1915, the

53. Untitled Document From left to right Philippe Levrier, Yvon Le Bars, Jacqueline de Guillenchmidt,Hélène fatou, Dominique Baudis, pierre Wiehn, Joseph Daniel, Francis Beck, http://www.csa.fr/rapport/synthese/membres_gb.htm

The members of the CSA and their responsibilities Nine Conseillers are nominated for a period of six years by presidential decree. Three of these members including the President are designated by the French President, three by the President of the Senate, and three by the President of the National Assembly. Three of the mandates are renewed every two years and the functions of the members of the Conseil are incompatible with any other term of office, the civil service or any other professional activity. Dominique Baudis has been the chairman of the CSA since 24 January 2001. The members of the CSA on a plenary session. From left to right: Philippe Levrier Yvon Le Bars Jacqueline de Guillenchmidt Dominique Baudis ... Francis Beck In order to make its work easier, the CSA set up fourteen work groups with responsibility for these shared between the council members. Each of the groups, led by both a chairman and a deputy chairman, studies dossiers before they are put before a plenary session. In addition, work involving other themes and the maintenance of relations with the major broadcasting companies is divided among council members.

54. CSA - Rapport D'activité 2002 pierre Wiehn. Langue française Mme Hélène fatou ;. • Relations avec les éditeurs de la presse nationale et http://www.csa.fr/rapport2002/donnees/rapport/VIII_conseil.htm

Introduction Les autorisations et les conventions Les avis Le Conseil Calendrier des faits marquants Les avis Les recommandations VIII - Le Conseil 3 - Les moyens du Conseil Les personnels Le budget 2002 me me me Jacqueline de Guillenchmidt, M. Yvon le Bars, M. Philippe Levrier et M. Pierre Wiehn. me me me me avis et recommandations cf. annexe me Janine Langlois-Glandier ; me Nouvelles technologies de l'information et de la communication Outre-mer me me Jacqueline de Guillenchmidt ; Programme et production audiovisuelle e Janine Langlois-Glandier ; Protection de l'enfance et de l'adolescence me me Jacqueline de Guillenchmidt ; me Radio me me me me M me M me Jacqueline de Guillenchmidt ; Canal+ : M me Janine Langlois-Glandier ; M. Pierre Wiehn ; Institut national de l'audiovisuel : M. Joseph Daniel ;

55. PopMatters Gazing out his window on the Place Pigalle in Paris, young Moses (pierre Drawn especially to the stunning fatou (Mata Gabin), a black prostitute who http://www.popmatters.com/film/reviews/m/monsieur-ibrahim.shtml

FILM archive - A B C D ... front page MONSIEUR IBRAHIM ET LES FLEURS DU CORAN Director : François Dupeyron Cast : Omar Sharif, Pierre Boulanger, Gilbert Melki, Anne Suarez, Isabelle Renauld (Sony Pictures Classics, 2003) Rated: R Release date : 5 December 2003 (limited) by Cynthia Fuchs PopMatters Film and TV Editor Omar Sharif in Monsieur Ibrahim et les fleurs du Coran e-mail this article print this article comment on this article Perplexities Gazing out his window on the Place Pigalle in Paris, young Moses (Pierre Boulanger) is distracted and uncertain. While Timmy Thomas' "Everybody Wants to Live Together" fills the soundtrack (the time is mid-1960s), Moses plans his first foray into sex, a date with one of the hookers who work Rue Bleue ("How much for a quickie?", he practices, posing with his fedora in the mirror). At the same time, he remains a child, utterly unable to resist his urge to toss a glass of water on his red-haired neighbor, Myriam (Lola Naynmark), practicing the latest dance steps in the alleyway between their homes. In this first sequence in Monsieur Ibrahim , Moses appears a typical teenaged boy, trying out his masculine prerogative and simultaneously unsure of what he wants. Adapted from Eric-Emmanuel Schmitt's novel (also a play) by director François Dupeyron and shrewdly shot (primarily with handheld camera) by Rémy Chevrin, the film delicately evokes the perplexities of male adolescence. Drawn especially to the stunning Fatou (Mata Gabin), a black prostitute who wears a blond wig and green summer dress, Moses approaches her; recognizing him as the boy who lives "over there," she turns him down, not believing his assertion that he's 16.

56. PopMatters Cast Omar Sharif, pierre Boulanger, Gilbert Melki, Anne Suarez, Drawn especiallyto the stunning fatou (Mata Gabin), a black prostitute who wears a http://www.popmatters.com/film/reviews/m/monsieur-ibrahim-dvd.shtml

FILM archive - A B C D ... front page MONSIEUR IBRAHIM ET LES FLEURS DU CORAN Director : François Dupeyron Cast : Omar Sharif, Pierre Boulanger, Gilbert Melki, Anne Suarez, Isabelle Renauld (Sony Pictures Classics, 2003) Rated: R DVD release date : 6 July 2004 (Columbia) by Cynthia Fuchs e-mail this article print this article comment on this article Sunshine Bouquet "Before this film was offered to me," says Omar Sharif on the commentary track for Monsieur Ibrahim , "I hadn't worked for five years, because I wasn't being offered any interesting material. And then out of the blue, one day, this script was sent to me." This from the man who acted in some of the grandest films of the last century Lawrence of Arabia Dr. Zhivago Funny Girl . Thank goodness that François Dupeyron thought to send him his screenplay, or Sharif might be most immediately remembered today for his prototypically "Arab" role in Hidalgo Later, he observes, "It's very difficult for me to find parts at my age, because I have this very peculiar accent which is neither French nor English nor Italian. I'm sort of a foreigner, I have to play foreigners. Now as I get old, it would be difficult to play anything but, I suppose old Arabs." Instead, he appears here as the title character, astute, curious, and especially, generous toward his young neighbor, Moses (Pierre Boulanger). Sharif remembers his costar fondly: "It's very difficult to find a child who's 13, 14, or who's interesting and who you don't actually hate, you know... And this boy has a natural charm and extraordinary talent. He understood everything right away."

57. List Of Scientists By Field Translate this page fatou, pierre Joseph Louis. Faujas de Saint-Fond, Barthélemy. Faulhaber, Johann.Favorsky, Alexei Yevgrafovich. Favre, pierre Antoine. Faye, Hervé http://www.indiana.edu/~newdsb/f.html

Fabbroni, Giovanni Valentino Mattia Fabbroni, Giovanni Valentino Mattia Fabre, Jean Henri Fabre, Jean Henri Fabrici, Girolamo Fabrici, Girolamo Fabricius, Johann Christian Fabry, Charles Fabry, Louis Fabry, Louis Fagnano dei Toschi, Giovanni Francesco Fagnano dei Toschi, Giulio Carlo Fahrenheit, Daniel Gabriel Fajans, Kasimir Falconer, Hugh Falloppio, Gabriele Fankuchen, Isidor Fankuchen, Isidor Fano, Gino Faraday, Michael Faraday, Michael Farey, John Farkas, Laszlo Farmer, John Bretland Farrar, John Farrar, John Farrar, John Fatou, Pierre Joseph Louis Faulhaber, Johann Favorsky, Alexei Yevgrafovich Favre, Pierre Antoine Featherstonhaugh, George William Fechner, Gustav Theodor Feddersen, Berend Wilhelm Fedorov, Evgenii Konstantinovich Fedorov, Evgenii Konstantinovich Fedorov, Evgenii Konstantinovich Feigl, Georg Feller, William Fenn, Wallace Osgood Fenneman, Nevin Melancthon Fenner, Clarence Norman Ferguson, James Ferguson, James Fermat, Pierre de Fermi, Enrico Fernald, Merritt Lyndon Ferrari, Ludovico Ferraris, Galileo Ferraris, Galileo Ferrein, Antoine

58. New Dictionary Of Scientific Biography Translate this page fatou, pierre Joseph Louis Faulhaber, Johann Feigl, Georg Fejér, Lipót Feller,William Fermat, pierre de Ferrari, Ludovico Ferrel, William http://www.indiana.edu/~newdsb/math.html

Make Suggestions Mathematics Abel, Niels Henrik Abraham Bar ?iyya Ha-Nasi Abu Kamil Shuja? Ibn Aslam Ibn Mu?ammad Ibn Shuja? Abu'l-Wafa? al-Buzjani, Mu?ammad Ibn Mu?ammad Ibn Ya?ya Ibn Isma?il Ibn al- ?Abbas Adams, John Couch Adelard of Bath Adrain, Robert Aepinus, Franz Ulrich Theodosius Agnesi, Maria Gaetana Aguilon, François d' A?mad Ibn Yusuf Aida Yasuaki Ajima Naonobu Akhiezer, Naum Il'ich Albert, Abraham Adrian Albert of Saxony Alberti, Leone Battista Aleksandrov, Pavel Sergeevich Alembert, Jean Le Rond d' Alzate y Ramírez, José Antonio Ampère, André-Marie Amsler, Jakob Anatolius of Alexandria Anderson, Oskar Johann Viktor Andoyer, Henri Angeli, Stefano Degli Anthemius of Tralles Antiphon Apollonius of Perga Appell, Paul Arbogast, Louis François Antoine Arbuthnot, John Archimedes Archytas of Tarentum Argand, Jean Robert Aristaeus Aristarchus of Samos Arnauld, Antoine Aronhold, Siegfried Heinrich Artin, Emil Atwood, George Autolycus of Pitane Auzout, Adrien

59. ICTCM-7 Abstract In the early twentieth century the French mathematicians pierre fatou and GastonJulia investigated iterating complex valued functions, but their studies http://archives.math.utk.edu/ICTCM/abs/7-SA5.html

Electronic Proceedings of the Seventh Annual Conference on Technology in Collegiate Mathematics CONTRIBUTED PAPER: 7-SA5 Iteration in First Semester Calculus James A. Walsh Department of Mathematics, Oberlin College Oberlin, OH 44074 Phone: (216)-775-8387; FAX: (216)-775-8124 E-mail: jimw@cs.oberlin.edu ABSTRACT With the advent of powerful personal computers a renewed focus on the ideas of iteration has appeared in the mathematics community. In the early twentieth century the French mathematicians Pierre Fatou and Gaston Julia investigated iterating complex valued functions, but their studies eventually came to a halt because of the amazing complexity of the sets they were considering without the aid of the computer. In recent years beautiful images of Julia sets and the Mandelbrot set seem to be appearing everywhere. This paper concerns itself with introducing the ideas of iterating a function of a single real variable in the first semester calculus course via the spreadsheet. Students are assigned three computer labs they complete as homework assignments using spreadsheets. The first lab investigates iterating linear maps f(x)=ax+b, where a and b are real parameters. An application is given in terms of a financial model of interest accruing in a savings account. The second lab investigates the dynamics of the logistic family f_k(x)=kx(1-x). This is a far more complicated family dynamically than the above family of linear maps, yet students investigate this complexity via the spreadsheet. In particular they discover the quadratic bifurcation diagram and learn about Feigenbaum's universal constant. An application is given to population models.

60. People Whose Names Are Embedded In Math Subject Classifcation Laurent is pierre A ( Laurent series of a function ), not the later Godfrey H (18781909) Ritz, Walter (1878-1929) fatou, pierre (1878-1952) Dehn, http://www.math.niu.edu/~rusin/known-math/98/MSC.names

Date: Sun, 6 Jun 1999 12:40:49 +0200 From: "Yuri I. Manin" Date: Thu, 28 Mar 2002 12:43:10 -0800 From: "Antreas P. Hatzipolakis" Cc: rusin@math.niu.edu, a_arakelov@yahoo.co.uk To: hyacinthos@yahoogroups.com Subject: Suren Arekelov This list is devoted to Triangle Geometry. However, from time to time, will be allowed discussions on themes of general interest. Especially when the geometric traffic is not too much. (like this day). Some time ago I asked for information (in fact I FWD-ed an e-mail of D. Rusin) about a notable mathematician who disappeared from the math. horizon. The mathematician is the algebraic geometer Suren Arakelov. Andrei Arakelov has kindly sent the following: > > Date: Thu, 28 Mar 2002 11:29:55 +0000 (GMT) > From: Andrei Arakelov > Subject: Suren Arakelov > To: Antreas P. Hatzipolakis Date: Sat, 05 Feb 2005 11:35:53 +0000 Message-ID:

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